A last minute no-show by the legendary leg-spinner at a press conference for his foundation earlier in the day added fuel to speculation in the British and Australian press that the celebrity couple had called it quits.
But Warne said on Wednesday evening that he and Hurley were working through their problems.
"Some of the reports re EH & me r absolute rubbish. Yes we're sorting through some (private) issues. But we're not throwing the towel in yet," he wrote on Twitter.
Half an hour earlier "Bedazzled" star Hurley had posted: "Apologies to loyal followers for Twitter silence on recent events. Too raw & personal to share right now."
The rumours were sparked by a lack of tweets between the pair with Hurley not sending Warne a 44th birthday message on September 13, although she was in England and he was in Australia visiting his three children.
Both of them are prolific social media users but Warne's last tweet to his 47-year-old fiancee was on August 30. She was reportedly due in Melbourne a week ago but has not turned up.
A Hurley tweet earlier this month that read "The more I know of man, the more I love my dog" only added to the speculation.
Warne had been due to attend a press conference in Melbourne Wednesday regarding his foundation, which helps raise funds for ill and underprivileged children, but he pulled out just 90 minutes before it was supposed to start.
Cricket Victoria blamed a "scheduling conflict" while Warne tweeted his apologies.
"Hey guys apologies about today & the late notice everyone!"
The Telegraph newspaper said journalists had been warned not to ask questions about the rumoured romance troubles, while other reports said Warne was lying low due to the supposed break-up.
The Sydney Morning Herald, a leading broadsheet, splashed the headline: "Shane Warne cancels ambassadors event, igniting Liz Hurley split rumours."
The tabloid Sydney Daily Telegraph went further, asking: "Is Shane Warne's ex-wife Simone Callahan behind his rumoured split with Liz Hurley?"
Warne and Hurley, the long-time former girlfriend of actor Hugh Grant, reportedly met in 2010 and confirmed their engagement via Twitter in 2011.